Dual-Blind Deconvolution for Overlaid Radar-Communications Systems

TL;DR

This paper introduces a novel dual-blind deconvolution approach for joint radar-communications systems sharing spectrum, enabling accurate parameter estimation despite unknown channels and signals.

Contribution

It develops a sum of multivariate atomic norms method and semidefinite programming framework for solving the highly ill-posed dual-blind deconvolution problem in spectral coexistence.

Findings

Achieves near-perfect recovery with sample complexity depending on the maximum of targets and paths logarithmically.

Applicable to scenarios with noise, unsynchronized transmission, and multiple emitters.

Demonstrates significant performance improvements in numerical experiments.

Abstract

The increasingly crowded spectrum has spurred the design of joint radar-communications systems that share hardware resources and efficiently use the radio frequency spectrum. We study a general spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown at the receiver. In this dual-blind deconvolution (DBD) problem, a common receiver admits a multi-carrier wireless communications signal that is overlaid with the radar signal reflected off multiple targets. The communications and radar channels are represented by continuous-valued range-time and Doppler velocities of multiple transmission paths and multiple targets. We exploit the sparsity of both channels to solve the highly ill-posed DBD problem by casting it into a sum of multivariate atomic norms (SoMAN) minimization. We devise a semidefinite program to estimate the unknown target and communications parameters using the theories of positive-hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show that the minimum number of samples required for near-perfect recovery is dependent on the logarithm of the maximum of number of radar targets and communications paths rather than their sum. We show that our SoMAN method and PhTP formulations are also applicable to more general scenarios such as unsynchronized transmission, the presence of noise, and multiple emitters. Numerical experiments demonstrate great performance enhancements during parameter recovery under different scenarios.